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3D family of curves

Al2000
1-Visitor

3D family of curves

A few days ago I learned reading old messages that one can draw a family of curves. I have no problem with family of curves on 2D but I was unable to suppress the return lines (fly back) in 3D. Is it possible to do it?



I'm appending a clip of the worksheet where I was doing my first trials. My goal is to plot the family of trajectories followed by several particles (10? 12?) with the same velocity but randomly dispersed in a small solid angle around Z axis.

I'm keeping the format because bold quantities (vectors) are not the same than normal quantities (scalars). In this clip only "w" (omega) appears in both roles, vector and magnitude.

Saludos,

Al
8 REPLIES 8

>...I was unable to suppress the return lines (fly back) in 3D. Is it possible to do it ?<<br> __________________________

Plot points, mesh finer if needed.

jmG

The 3D plot has no provision for a single plot to hae disconnected componenents. You need to make separate plots if you need that. As you seem to have already discovered.

For this specific case, since all the lines start at the same point you can draw each line twice, once forward and then backwards. Then you have a single connected figure.

Once you've gone to the trouble of applying decent formatting, why would you even consider removing it? There is no need to apologize for having a neatly formatted sheet.

Just as there is no need to apologize for using ORIGIN=1. As long as you recognize that some of us (like me) work with ORIGIN=0 so that there are compatibility issues, you are well within your rights to use whatever ORIGIN (or other settings) you choose. Unless and until such settings actually cause trouble (most likely the result tolerances, that can cause some normal physical constants, like the electron charge or electron mass, to display as zeros).
__________________
Tom Gutman
Al2000
1-Visitor
(To:Al2000)

Thanks guys, I'll try both approachs...

Peace,

Al
StuartBruff
23-Emerald III
(To:Al2000)

On 8/22/2009 12:25:40 AM, Al2000 wrote:
>A few days ago I learned
>reading old messages that one
>can draw a family of curves. I
>have no problem with family of
>curves on 2D but I was unable
>to suppress the return lines
>(fly back) in 3D. Is it
>possible to do it?

Yes. plot the return lines on a different 'level'
(z-depth) to the main plots and use a colormap that
hides that level.

See http://collab.mathsoft.com/read?94485,12 ,
particularly the worksheet
http://collab.mathsoft.com/upload/Test%20-
%20Graphics%2002a.mcd

Stuart
Al2000
1-Visitor
(To:Al2000)

Jean: I tested your idea and it works well (as I was expecting). There is only the need of tweaking the spacing of points. The resulting curves are somewhat bold but you can adjust the point size to account for that. Of course you need to be able of generate the points and you need to generate a lot of extra points. In my little example 4 times more points.

Tom: Easy done just stacking each matrix with its reverse. Of course as you anticipated if the family of curves don't start in the same point then ugly lines connecting each trace are plotted. In my case i was able to suppress those lines just adjusting a little the lower limit of Z axis. The lines are bolded a little and again you can adjust the line width to correct.

Jean indirectly suggested me another solution for this case: adding some extra points to "route" the fly back outside the clipping box. This works in my case 'cause no trace starts and ends inside the clipping box.



Stuart: I was unable to see the sheet you suggested. My version of MC is old, ver. 2001.

Saludos,

Al
StuartBruff
23-Emerald III
(To:Al2000)

On 8/22/2009 4:40:28 AM, Al2000 wrote:
== Stuart: I was unable to see the sheet you
suggested. My version of MC is old, ver. 2001.

>Jean: I tested your idea and it works well (as I was expecting). There is only the need of tweaking the spacing of points. The resulting curves are somewhat bold but you can adjust the point size to account for that. Of course you need to be able of generate the points and you need to generate a lot of extra points. In my little example 4 times more points. <<br> ________________________

Your project start solid right away, pushing 4 nails in a single blow ! The other point is 4 Users, sen instead of the built-in sin. All variables can be "variables", that is no critics just that it complicates matters. Added a single & simple motion in space that you might be able to make "Lorentz". Also added the DE solution from Mathsoft

Jean

... with enough points you get a nice plot.

Jean
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